Texture Reconstruction guided by the Histogram of a High-Resolution patch

Mireille El Gheche (1, 2) , Jean-François Aujol (1) , Yannick Berthoumieu (2) , Charles-Alban Deledalle (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMS - Laboratoire de l'intégration, du matériau au système

In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches, that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to state-of-the-art algorithms for solving similar problems.

Mots clés: Super-Resolution; Texture Synthesis; Texture Reconstruction; Wasserstein distance; Histograms; Nonlocal regularization; Proximal algorithms; nonconvex optimization

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]

Mireille El Gheche, Jean-François Aujol, Yannick Berthoumieu, Charles-Alban Deledalle. Texture Reconstruction guided by the Histogram of a High-Resolution patch. 2016. ⟨hal-01276582v1⟩